# SOLVING A LINEAR SYSTEM BY SUBSTITUTION WORKSHEET

## About "Solving a linear system by substitution worksheet"

Solving a linear system by substitution worksheet :

Worksheet is on solving a linear system by substitution is much useful to the students who would like to practice solving system of simultaneous linear equations in two variables.

## Steps in method of substitution

Step 1 :

Solve one of the equations for one of its variables.

Step 2 :

Substitute the expression from step 1 into the other equation and solve for the other variable.

Step 3 :

Substitute the value from step 2 into either original equation and solve to find the value of the variable in step 1.

## Solving a linear system by substitution worksheet - Problems

1.  Solve the system of linear equations by substitution. Check your answer by graphing.

4x + y  =  8

-3x + y  =  1

2.  Solve the system of linear equations by substitution. Check your answer by graphing.

x + y  =  8

2x + y  =  11 ## Solving a linear system by substitution worksheet - Solution

Problem 1 :

Solve the system of linear equations by substitution. Check your answer by graphing.

4x + y  =  8

-3x + y  =  1

Solution :

Step 1 :

Solve an equation for one variable.

Select one of the equation, say -3x + y  =  1.

Solve for the variable y in terms of x.

Add 3x on both sides.

(-3x + y) + 3x  =  (1) + 3x

-3x + y + 3x  =  1 + 3x

Simplify.

y  =  1 + 3x

Step 2 :

Substitute the expression for y in the other equation and solve.

4x + y  =  8

4x + (1 + 3x)  =  8

Combine like terms.

7x + 1  =  8

Subtract 1 from both sides.

7x  =  7

Divide both sides by 7.

7x / 7  =  7 / 7

x  =  1

Step 3 :

Substitute the value of x we got above (x = 1) into one of the equations and solve for the other variable, y.

4x + y  =  8

4(1) + y  =  8

4 + y  =  8

Subtract 4 from both sides.

y  =  8

Hence, the solution of the system is (1, 8).

Step 4 :

Check the solution by graphing.

To graph the equations, write them in slope-intercept form.

That is,

y  =  mx + b

4x + y  =  8

y  =  - 4x + 8

Slope  =  - 4

y-intercept  =  8

-3x + y  =  1

y  =  3x + 1

Slope  =  3

Y-intercept  =  1 The point of intersection is (1, 4).

Problem 2 :

Solve the system of linear equations by substitution. Check your answer by graphing.

x + y  =  8

2x + y  =  11

Solution :

Step 1 :

Solve an equation for one variable.

Select one of the equation, say x + y  =  8.

Solve for the variable y in terms of x.

Subtract x from both sides.

(x + y) - x  =  (8) - x

x + y - x  =  8 - x

Simplify.

y  =  8 - x

Step 2 :

Substitute the expression for y in the other equation and solve.

2x + y  =  11

2x + (8 - x)  =  11

Combine like terms.

x + 8  =  11

Subtract 8 from both sides.

x  =  3

Step 3 :

Substitute the value of x we got above (x = 3) into one of the equations and solve for the other variable, y.

x + y  =  8

3 + y  =  8

Subtract 3 from both sides.

y  =  5

Hence, the solution of the system is (3, 5).

Step 4 :

Check the solution by graphing.

To graph the equations, write them in slope-intercept form.

That is,

y  =  mx + b

x + y  =  8

y  =  - x + 8

Slope  =  - 1

y-intercept  =  8

2x + y  =  11

y  =  -2x + 11

Slope  =  -2

Y-intercept  =  11 The point of intersection is (1, 4). After having gone through the stuff given above, we hope that the students would have understood "Solving a linear system by substitution worksheet".

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